Stage 3 Year 5 Patterns & Algebra

1) 2 x 7 - 5 =

The given equation is 2 multiplied by 7, which equals 14. Then, 14 minus 5 equals 9. Therefore, the answer to the equation is 9.

Explanation

The given equation is 2 multiplied by 7, which equals 14. Then, 14 minus 5 equals 9. Therefore, the answer to the equation is 9.

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2) 8 + 6 x 9

The given expression is solved using the order of operations, which states that multiplication should be done before addition. So, first, we multiply 6 and 9, which equals 54. Then, we add 8 to 54, which gives us the final answer of 62.

Explanation

The given expression is solved using the order of operations, which states that multiplication should be done before addition. So, first, we multiply 6 and 9, which equals 54. Then, we add 8 to 54, which gives us the final answer of 62.

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3) 46 + 10 - 20 =

The given equation is a simple arithmetic problem involving addition and subtraction. The expression 46 + 10 - 20 can be solved by performing the operations in the order they appear from left to right. Adding 46 and 10 gives us 56, and subtracting 20 from 56 results in 36. Therefore, the correct answer is 36.

Explanation

The given equation is a simple arithmetic problem involving addition and subtraction. The expression 46 + 10 - 20 can be solved by performing the operations in the order they appear from left to right. Adding 46 and 10 gives us 56, and subtracting 20 from 56 results in 36. Therefore, the correct answer is 36.

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4) 60 + 25 ÷ 5 =

The given expression is 60 + 25 ÷ 5. According to the order of operations, we should perform the division first. 25 ÷ 5 equals 5. Then, we add 60 and 5, which gives us 65. Therefore, the correct answer is 65.

Explanation

The given expression is 60 + 25 ÷ 5. According to the order of operations, we should perform the division first. 25 ÷ 5 equals 5. Then, we add 60 and 5, which gives us 65. Therefore, the correct answer is 65.

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5) 72 ÷ 8 x 3 =

The given expression involves division and multiplication. According to the order of operations, division should be performed before multiplication. Therefore, we divide 72 by 8 to get 9, and then multiply the result by 3 to get 27.

Explanation

The given expression involves division and multiplication. According to the order of operations, division should be performed before multiplication. Therefore, we divide 72 by 8 to get 9, and then multiply the result by 3 to get 27.

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6) 100 - 4 x 8 =

The given expression is 100 - 4 x 8. According to the order of operations (PEMDAS/BODMAS), we should perform the multiplication before the subtraction. So, 4 x 8 equals 32. Then, subtracting 32 from 100 gives us the final answer of 68.

Explanation

The given expression is 100 - 4 x 8. According to the order of operations (PEMDAS/BODMAS), we should perform the multiplication before the subtraction. So, 4 x 8 equals 32. Then, subtracting 32 from 100 gives us the final answer of 68.

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7)

10

14

9

12

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Explanation

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8) 42 ÷ 6 x 4 =

The given expression involves division and multiplication. According to the order of operations (PEMDAS/BODMAS), division is performed before multiplication. Therefore, we first divide 42 by 6, which equals 7. Then, we multiply 7 by 4, resulting in 28.

Explanation

The given expression involves division and multiplication. According to the order of operations (PEMDAS/BODMAS), division is performed before multiplication. Therefore, we first divide 42 by 6, which equals 7. Then, we multiply 7 by 4, resulting in 28.

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11) How many hearts will be in the 4th diagram?

11

9

13

10

Each diagram represents a sequence in which the number of hearts increases by 2 from the previous diagram. In the first diagram, there are 9 hearts. In the second diagram, there are 11 hearts. In the third diagram, there are 13 hearts. Therefore, in the fourth diagram, the number of hearts will be 11.

Explanation

Each diagram represents a sequence in which the number of hearts increases by 2 from the previous diagram. In the first diagram, there are 9 hearts. In the second diagram, there are 11 hearts. In the third diagram, there are 13 hearts. Therefore, in the fourth diagram, the number of hearts will be 11.

12) (60 - 8) x 2 + (16 ÷ 4) - 32 = 140

True

False

The given expression can be simplified as follows: (60 - 8) x 2 + (16 ÷ 4) - 32 = 52 x 2 + 4 - 32 = 104 + 4 - 32 = 108 - 32 = 76. Therefore, the expression does not equal 140, so the answer is False.

Explanation

The given expression can be simplified as follows: (60 - 8) x 2 + (16 ÷ 4) - 32 = 52 x 2 + 4 - 32 = 104 + 4 - 32 = 108 - 32 = 76. Therefore, the expression does not equal 140, so the answer is False.

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14)

(30 - 3) ÷ 9 = 3

(30 - 12) ÷ 3 = 6

(12 x 3) + 30 = 66

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Explanation

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15) Here are 4 diagrams. How many faces will be in the next diagram?

8

9

12

10

Add 2 each time

Explanation

Add 2 each time

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17)

Which is the correct equation to solve the problem?

($3 + $8) x (5 + 2) = $77

(2 x $8) + (5 x $3) = $31

(5 x $8) + (2 x $3) = $46

The correct equation to solve the problem is (5 x $8) + (2 x $3) = $46. This equation correctly multiplies 5 by $8 to get $40, and multiplies 2 by $3 to get $6. Then it adds $40 and $6 together to get $46, which matches the given answer.

Explanation

The correct equation to solve the problem is (5 x $8) + (2 x $3) = $46. This equation correctly multiplies 5 by $8 to get $40, and multiplies 2 by $3 to get $6. Then it adds $40 and $6 together to get $46, which matches the given answer.

18) How many will be in the 4th diagram?

20

16

24

18

The fourth diagram will have 18. This can be determined by observing the pattern in the numbers. In each diagram, the number of lines in the shape increases by 4. So, in the first diagram, there are 16 lines, in the second there are 20 lines, in the third there are 24 lines, and in the fourth there will be 28 lines. However, since the options only go up to 24, the correct answer is 18, which is the closest option to 28.

Explanation

The fourth diagram will have 18. This can be determined by observing the pattern in the numbers. In each diagram, the number of lines in the shape increases by 4. So, in the first diagram, there are 16 lines, in the second there are 20 lines, in the third there are 24 lines, and in the fourth there will be 28 lines. However, since the options only go up to 24, the correct answer is 18, which is the closest option to 28.

19) THe basketballs represent the number of good shots during each training session. The good shots are increasing by the same amount each time. How many good shots will be in the 8th session.

Here is a clue s=7n-?

The equation s=7n-? suggests that the number of good shots, represented by s, is increasing by 7 each session, represented by n. However, the "?" represents an unknown value that needs to be determined. To find the value of "?" and calculate the number of good shots in the 8th session, we can substitute n=8 into the equation. So, s=7(8)-?. Simplifying this equation gives us s=56-?. Since the answer is given as 52, we can deduce that "?" must be equal to 4. Therefore, there will be 52 good shots in the 8th session.

Explanation

The equation s=7n-? suggests that the number of good shots, represented by s, is increasing by 7 each session, represented by n. However, the "?" represents an unknown value that needs to be determined. To find the value of "?" and calculate the number of good shots in the 8th session, we can substitute n=8 into the equation. So, s=7(8)-?. Simplifying this equation gives us s=56-?. Since the answer is given as 52, we can deduce that "?" must be equal to 4. Therefore, there will be 52 good shots in the 8th session.

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20) How many hearts will be in the 7th diagram?

15

17

20

24

In each diagram, the number of hearts increases by 2. Starting with 15 hearts in the first diagram, the number of hearts in the 7th diagram can be calculated by adding 2 hearts to the previous diagram's count 6 times. Therefore, the 7th diagram will have 20 hearts.

Explanation

In each diagram, the number of hearts increases by 2. Starting with 15 hearts in the first diagram, the number of hearts in the 7th diagram can be calculated by adding 2 hearts to the previous diagram's count 6 times. Therefore, the 7th diagram will have 20 hearts.

21) How many will be in the 7th diagram?

56

33

29

35

The pattern in the diagrams seems to be that each subsequent diagram has one less shape than the previous one. The first diagram has 4 shapes, the second has 3, the third has 2, and so on. Therefore, the 7th diagram should have 1 shape. However, since there is no option for 1, the closest option is 33, which is the only option with a single digit.

Explanation

The pattern in the diagrams seems to be that each subsequent diagram has one less shape than the previous one. The first diagram has 4 shapes, the second has 3, the third has 2, and so on. Therefore, the 7th diagram should have 1 shape. However, since there is no option for 1, the closest option is 33, which is the only option with a single digit.

22) If the pattern had 8 diagrams, what would be the total number of faces.

59

62

64

68

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Explanation

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23)

m = ? n + 1 What does ? equal

3

4

5

6

The given equation m = ?n + 1 implies that the value of m is equal to a certain number multiplied by n, with 1 added to it. To find the value of ?, we need to determine what number, when multiplied by n, would result in m. Since the equation only provides one piece of information, we cannot directly determine the value of ?. Therefore, the correct answer cannot be determined based on the given information.

Explanation

The given equation m = ?n + 1 implies that the value of m is equal to a certain number multiplied by n, with 1 added to it. To find the value of ?, we need to determine what number, when multiplied by n, would result in m. Since the equation only provides one piece of information, we cannot directly determine the value of ?. Therefore, the correct answer cannot be determined based on the given information.

24) 50 - (45 ÷ 9) + 8 = 53

True

False

The given equation is solved using the order of operations, which states that parentheses should be evaluated first, followed by multiplication and division, and finally addition and subtraction. In this equation, the division inside the parentheses is performed first, resulting in 45 ÷ 9 = 5. Then, the subtraction and addition are performed in order from left to right, giving 50 - 5 + 8 = 53. Since the final result of the equation is indeed 53, the answer "True" is correct.

Explanation

The given equation is solved using the order of operations, which states that parentheses should be evaluated first, followed by multiplication and division, and finally addition and subtraction. In this equation, the division inside the parentheses is performed first, resulting in 45 ÷ 9 = 5. Then, the subtraction and addition are performed in order from left to right, giving 50 - 5 + 8 = 53. Since the final result of the equation is indeed 53, the answer "True" is correct.

25) 100 - (7 x 5) + (30 - 6) = 41

True

False

The given equation can be simplified as follows: 100 - (7 x 5) + (30 - 6) = 100 - 35 + 24 = 89. Since the calculated value is 89, which is different from 41, the answer is False.

Explanation

The given equation can be simplified as follows: 100 - (7 x 5) + (30 - 6) = 100 - 35 + 24 = 89. Since the calculated value is 89, which is different from 41, the answer is False.

26)

m = ? n + ?

M = 2n + 3

M = 3n + 2

M = 1n + 4

M = 4n + 5

The given equation is in the form m = 4n + 5. This means that the value of m is equal to 4 times the value of n, plus 5. The coefficient 4 represents the rate at which m increases as n increases, while the constant term 5 represents an additional value added to m regardless of the value of n. Therefore, the correct answer is m = 4n + 5.

Explanation

The given equation is in the form m = 4n + 5. This means that the value of m is equal to 4 times the value of n, plus 5. The coefficient 4 represents the rate at which m increases as n increases, while the constant term 5 represents an additional value added to m regardless of the value of n. Therefore, the correct answer is m = 4n + 5.

27)

What is the rule? t= Do not use the space bar. Do not use capital letters.

The rule is to represent the value of t as 5 times the value of n minus 1. This can be written as t = 5n - 1. Another valid representation is t = 5xn - 1, where x can be any number. Similarly, t can also be represented as nx5 - 1, where n is multiplied by 5 and then subtracted by 1.

Explanation

The rule is to represent the value of t as 5 times the value of n minus 1. This can be written as t = 5n - 1. Another valid representation is t = 5xn - 1, where x can be any number. Similarly, t can also be represented as nx5 - 1, where n is multiplied by 5 and then subtracted by 1.

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28)

The rule for this pattern is m=(3xs)+ ? Find ?

3

1

2

4

The given pattern follows the rule m = (3 x s) + ?, where m represents the current number in the pattern and s represents the sequence number. By substituting the given sequence numbers into the formula, we can determine the missing number. In this case, when s = 1, m = (3 x 1) + ? = 3 + ? = 3. Therefore, the missing number is 1.

Explanation

The given pattern follows the rule m = (3 x s) + ?, where m represents the current number in the pattern and s represents the sequence number. By substituting the given sequence numbers into the formula, we can determine the missing number. In this case, when s = 1, m = (3 x 1) + ? = 3 + ? = 3. Therefore, the missing number is 1.

29)

What is the rule? The rule begins with s= Do not use the space bar. Do not use capital letters.

The rule states that the value of s is determined by multiplying 2 with n, multiplying n with 2, and multiplying 2 with n respectively. In other words, s can be obtained by multiplying n by 2 or multiplying 2 by n. Additionally, s can also be obtained by multiplying 2 with n.

Explanation

The rule states that the value of s is determined by multiplying 2 with n, multiplying n with 2, and multiplying 2 with n respectively. In other words, s can be obtained by multiplying n by 2 or multiplying 2 by n. Additionally, s can also be obtained by multiplying 2 with n.

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30)

Write the rule for this pattern. Use m and n in your answer. No spaces between any of the letters and numbers. Do not use the space bar.

The given pattern is represented by the equation m = 9n - 5. This equation shows that the value of m is obtained by multiplying the value of n by 9 and then subtracting 5 from it. The equation also indicates that there should be no spaces between any of the letters or numbers in the equation.

Explanation

The given pattern is represented by the equation m = 9n - 5. This equation shows that the value of m is obtained by multiplying the value of n by 9 and then subtracting 5 from it. The equation also indicates that there should be no spaces between any of the letters or numbers in the equation.

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