CBSE Class 7 Mathematics Arithmetic Expressions Worksheet Set 01

Very Short Answer Questions

Question 1. What is meant by the value of an arithmetic expression? Give one example.
Answer:
The value of an expression is the single number that the expression works out to.
Example: the value of 13 + 2 is 15.

Teacher's Note:
1. Give the meaning and an example.
2. Write it with the = sign: 13 + 2 = 15.

Question 2. Write an arithmetic expression for “the product of 7 and 13” and find its value.
Answer:
Expression: 7 × 13; value = 91.

Teacher's Note:
1. Product means multiply.
2. 7 × 13 = 70 + 21 = 91.

Question 3. Write any two different arithmetic expressions whose value is 18.
Answer:
For example, 12 + 6 and 3 × 6 both have the value 18.
(Others such as 20 − 2 or 36 ÷ 2 are also correct.)

Teacher's Note:
1. Many expressions can share one value.
2. Check that each one really gives 18.

Question 4. A pen costs ₹18. Write an expression for the cost of 6 such pens and find its value.
Answer:
Expression: 6 × 18; value = ₹108.

Teacher's Note:
1. 6 equal costs means multiply.
2. 6 × 18 = 60 + 48 = 108.

Question 5. Place the correct sign (<, > or =) between the expressions 14 + 9 and 8 × 3.
Answer:
14 + 9 = 23 and 8 × 3 = 24, so 14 + 9 < 8 × 3.

Teacher's Note:
1. Compare the values.
2. The open side of the sign faces the bigger number.

Question 6. Write the two terms of the expression 47 − 19.
Answer:
47 − 19 = 47 + (−19), so the terms are 47 and −19.

Teacher's Note:
1. Subtraction means adding the inverse.
2. The minus sign stays with 19.

Question 7. Find the value of 25 + (6 × 7).
Answer:
Bracket first: 6 × 7 = 42. Then 25 + 42 = 67.

Teacher's Note:
1. Brackets are always done first.
2. Then add.

Question 8. Why is a bracket needed in an expression such as 30 + 5 × 4 when it describes a real situation?
Answer:
Without a bracket the order of the operations is not clear, and someone may add 30 and 5 first.
Writing 30 + (5 × 4) shows clearly that 5 × 4 has to be worked out first.

Teacher's Note:
1. A bracket gives the expression only one meaning.
2. It is like a comma in a sentence.

Question 9. Write 9 + 15 − 4 as a sum of its terms and list the terms.
Answer:
9 + 15 − 4 = 9 + 15 + (−4).
Terms: 9, 15 and −4 (value 20).

Teacher's Note:
1. Turn the subtraction into adding −4.
2. Each term keeps its own sign.

Question 10. State the commutative property of addition in your own words.
Answer:
Swapping two terms of a sum does not change the value: Term 1 + Term 2 = Term 2 + Term 1.
Example: 6 + (−4) = (−4) + 6 = 2.

Teacher's Note:
1. Commute means to move or swap.
2. It works for negative terms too.

Question 11. Remove the brackets from 26 + (14 − 9) and find its value.
Answer:
The bracket follows a + sign, so the signs stay the same: 26 + 14 − 9 = 31.

Teacher's Note:
1. Plus before a bracket: no sign changes.
2. Check: 26 + 5 = 31.

Question 12. Fill in the blank: 3 × (5 + 6) = 3 × 5 + 3 × ____.
Answer:
The blank is 6, since 3 × (5 + 6) = 3 × 5 + 3 × 6 = 15 + 18 = 33.

Teacher's Note:
1. Multiply 3 with each term inside.
2. This is the distributive property.

Question 13. Without finding the values, say which is greater, 512 + 347 or 511 + 349, and why.
Answer:
In 511 + 349 the first number is 1 less but the second number is 2 more, so its total is 1 more.
So 511 + 349 is greater (860 against 859).

Teacher's Note:
1. Compare the changes, not the totals.
2. Net change = −1 + 2 = +1.

Question 14. Arrange these expressions in increasing order of their values: 72 − 25, 8 × 6, 90 ÷ 2.
Answer:
72 − 25 = 47, 8 × 6 = 48 and 90 ÷ 2 = 45.
Increasing order: 90 ÷ 2 < 72 − 25 < 8 × 6.

Teacher's Note:
1. Find each value first.
2. Increasing means smallest first.

Question 15. Find the value of 45 − 6 × 5 + 12 ÷ 4 by first writing its terms.
Answer:
Terms: 45, −6 × 5 and 12 ÷ 4.
Value = 45 − 30 + 3 = 18.

Teacher's Note:
1. Evaluate each term, then add.
2. × and ÷ stay inside their terms.

Question 16. Remove the brackets from 60 − (25 − 8) and find its value.
Answer:
A minus sign comes before the bracket, so each sign inside changes: 60 − 25 + 8 = 43.

Teacher's Note:
1. −8 inside becomes +8 outside.
2. Check: 60 − 17 = 43.

Question 17. A shopkeeper has 5 boxes with 12 candles in each box, and 7 loose candles. Write an expression for the total number of candles and find its value.
Answer:
Expression: 5 × 12 + 7 (terms 5 × 12 and 7).
Value = 60 + 7 = 67 candles.

Teacher's Note:
1. Boxes give a product; loose candles are added.
2. The product is one term.

Question 18. Use the distributive property to find 98 × 7.
Answer:
98 × 7 = (100 − 2) × 7 = 100 × 7 − 2 × 7 = 700 − 14 = 686.

Teacher's Note:
1. 98 is close to 100.
2. Multiply both 100 and 2 by 7.

Question 19. Insert one pair of brackets at the correct place so that 40 − 12 + 8 = 20.
Answer:
40 − (12 + 8) = 20, since 40 − 20 = 20.
(Without brackets, 40 − 12 + 8 = 36.)

Teacher's Note:
1. Try brackets in each place and check.
2. Both 12 and 8 must be taken away.

Question 20. Are 87 − 46 + 109 and (87 − 46) + 109 equal? Give the reason.
Answer:
Yes, they are equal. The bracket is not after a minus sign, so both have the same terms 87, −46 and 109.
Each value is 150.

Teacher's Note:
1. Same terms give the same value.
2. Only a minus before a bracket changes signs.

Question 21. Using reasoning about terms only, fill in the blank: 328 + ____ = 324 + 150.
Answer:
328 is 4 more than 324, so the other number must be 4 less than 150.
The blank is 146 (both sides equal 474).

Teacher's Note:
1. Balance the change in one term with the other.
2. +4 in one term needs −4 in the other.

Question 22. A fruit seller sells 8 kg of apples and 6 kg of guavas every day. Write an expression for the quantity sold in a week and find its value.
Answer:
Expression: 7 × (8 + 6).
Value = 7 × 14 = 98 kg in a week.

Teacher's Note:
1. A week has 7 days.
2. 7 × 8 + 7 × 6 gives the same answer.

Question 23. Find the value of 110 − (30 − (12 + 8)).
Answer:
Innermost bracket: 12 + 8 = 20; then 30 − 20 = 10.
Value = 110 − 10 = 100.

Teacher's Note:
1. Work from the innermost bracket outwards.
2. Write each step on a new line.

Question 24. Which is greater, 19 × 36 − 14 or 19 × (36 − 14)? Give a reason.
Answer:
In 19 × 36 − 14, 19 is taken 36 times and only 14 is removed: 684 − 14 = 670.
In 19 × (36 − 14), 19 is taken just 22 times: 19 × 22 = 418.
So 19 × 36 − 14 is greater.

Teacher's Note:
1. The bracket changes what is multiplied.
2. Compare 36 groups with 22 groups.

Question 25. Rani subtracts 9 from any number by subtracting 10 and then adding 1. Explain why her method always gives the correct answer.
Answer:
9 = 10 − 1, so for any number n, n − 9 = n − (10 − 1) = n − 10 + 1.
Removing the bracket after the minus sign turns −1 into +1, which is exactly Rani's method.

Teacher's Note:
1. Taking away 10 removes 1 too many.
2. So 1 is added back.

Question 26. Without evaluating fully, state whether 42 × (30 − 18) is greater than, less than or equal to 41 × (29 − 18), and give the reason.
Answer:
42 is bigger than 41, and 30 − 18 = 12 is bigger than 29 − 18 = 11.
A bigger number taken a bigger number of times gives more, so 42 × (30 − 18) is greater (504 against 451).

Teacher's Note:
1. Compare both factors.
2. Both factors bigger means a bigger product.

Question 27. Using the numbers 3, 4 and 7 exactly once each, with +, − and brackets as needed, write two expressions that have different values. Give both values.
Answer:
7 − (4 − 3) = 7 − 4 + 3 = 6 and 7 − 4 − 3 = 0.
(Other correct pairs are possible, e.g. 3 + 4 + 7 = 14.)

Teacher's Note:
1. A bracket can change the value.
2. Use each number exactly once.

Question 28. Given that 64 × 25 = 1600, find 64 × 26 without doing the full multiplication.
Answer:
64 × 26 = 64 × (25 + 1) = 64 × 25 + 64 × 1 = 1600 + 64 = 1664.

Teacher's Note:
1. One more group of 64.
2. Use the distributive property.

Question 29. Explain, using the idea of terms, why 73 − 14 + 1 and 73 − (14 − 1) have the same value.
Answer:
A minus before the bracket changes every sign inside, so 73 − (14 − 1) = 73 − 14 + 1.
Both have the terms 73, −14 and 1, so both have the same value, 60.

Teacher's Note:
1. Same terms mean the same value.
2. −1 inside becomes +1 outside.

Question 30. Sunil earns ₹18,000 every month and spends ₹7,000 on rent and ₹4,000 on food each month. Write an expression for his savings in one year and find its value.
Answer:
Savings in a year = 12 × 18000 − 12 × (7000 + 4000) [or 12 × (18000 − 7000 − 4000)].
= 216000 − 132000 = ₹84,000.

Teacher's Note:
1. A year has 12 months.
2. Saving per month is ₹7,000.