CBSE Class 7 Mathematics Arithmetic Expressions Assignment Set 01

Short Answer Questions

Question 1. What is an arithmetic expression? What is meant by the value of an expression? Read the expression 24 − 9 in words in two different ways and write its value.
Answer:
An arithmetic expression is a mathematical phrase made of numbers joined by the operations +, −, × and ÷, for example 13 + 2 or 12 × 5.
The value of an expression is the single number it works out to.
24 − 9 can be read as “24 minus 9” or “the difference of 24 and 9”.
Its value is 15, so we write 24 − 9 = 15.
In simple words: An expression is numbers joined by operations, and its value is the one number it gives.

Teacher's Note:
1. Answer all four parts.
2. “9 less than 24” is another correct reading.

Question 2. Using two numbers and any one of the four operations +, −, × and ÷ each time, write four different expressions whose value is 18. Show the value of each expression.
Answer:
Addition: 12 + 6 = 18
Subtraction: 25 − 7 = 18
Multiplication: 3 × 6 = 18
Division: 36 ÷ 2 = 18
Different expressions can have the same value 18, so many more such expressions are possible.
In simple words: Many expressions using different operations can all give 18.

Teacher's Note:
1. Use each operation once.
2. Check every value.

Question 3. Write an expression for each situation and find its value.
(i) Sunita buys 6 notebooks and each notebook costs ₹32.
(ii) Ravi had ₹500 in his purse and spent ₹145 on a gift.
Answer:
(i) Cost = 6 × 32 = 192, so Sunita pays ₹192.
(ii) Money left = 500 − 145 = 355, so Ravi has ₹355 left.
In each case the situation is first written as an expression and then evaluated.
In simple words: Turn the story into an expression, then work it out.

Teacher's Note:
1. Equal costs mean multiply.
2. Spending means subtract.

Question 4. Put the correct sign <, > or = between each pair of expressions by reasoning, not by long calculation. Give your reason in one line each.
(i) 348 + 256 and 349 + 255
(ii) 512 − 128 and 512 − 130
Answer:
(i) 348 + 256 = 349 + 255. The first number goes up by 1 and the second comes down by 1, so the changes cancel.
(ii) 512 − 128 > 512 − 130. Both start from 512, but more is taken away in the second, so less is left (384 against 382).
In simple words: Compare how each number changes instead of working out the full answers.

Teacher's Note:
1. In a sum, +1 and −1 cancel.
2. Taking away more leaves less.

Question 5. Why do we need brackets in an arithmetic expression? Find the values of 40 + (6 × 7) and (40 + 6) × 7, and state what your answers show.
Answer:
Brackets show which part of an expression must be worked out first, so that the expression has only one meaning.
40 + (6 × 7) = 40 + 42 = 82
(40 + 6) × 7 = 46 × 7 = 322
The same numbers and signs give very different values, so the position of the brackets decides the value.
In simple words: Brackets tell us what to do first, and moving them can change the answer.

Teacher's Note:
1. Always work out the bracket first.
2. Compare the two answers in your conclusion.

Question 6. Write the expression 15 − 8 + 6 as a sum of its terms. List all the terms and then find the value of the expression.
Answer:
Subtracting a number is the same as adding its inverse, so 15 − 8 + 6 = 15 + (−8) + 6.
Terms: 15, −8 and 6.
Value = 15 − 8 + 6 = 7 + 6 = 13.
In simple words: Change −8 into + (−8), list the terms and add them.

Teacher's Note:
1. The minus sign stays with 8.
2. Terms can be added in any order.

Question 7. Identify the terms of the expression 7 × 4 − 20 ÷ 5 + 9 and hence find its value. Explain in one line why 7 × 4 is counted as a single term.
Answer:
As a sum of terms: 7 × 4 − 20 ÷ 5 + 9 = (7 × 4) + (−20 ÷ 5) + 9.
Terms: 7 × 4, −20 ÷ 5 and 9.
Value = 28 − 4 + 9 = 33.
7 × 4 is one term because terms are separated only by a + sign, and there is no + sign inside 7 × 4.
In simple words: Find the terms, work out each one, then add them.

Teacher's Note:
1. × and ÷ never break a term.
2. Evaluate the terms before adding.

Question 8. State the commutative property of addition and the associative property of addition. Give one example of each using at least one negative term.
Answer:
Commutative property: swapping two terms does not change the sum. Example: (−6) + 11 = 11 + (−6) = 5.
Associative property: grouping the terms in a different way does not change the sum. Example: (3 + (−8)) + 5 = 3 + ((−8) + 5), as both sides equal 0.
In simple words: Changing the order or the grouping of terms does not change their sum.

Teacher's Note:
1. Swap = commutative; regroup = associative.
2. Show both sides are equal.

Question 9. Remove the brackets and then simplify. Show the sign of every term clearly.
(i) 52 − (18 + 9)
(ii) 52 − (18 − 9)
Answer:
A bracket after a minus sign changes the sign of every term inside it.
(i) 52 − (18 + 9) = 52 − 18 − 9 = 34 − 9 = 25.
(ii) 52 − (18 − 9) = 52 − 18 + 9 = 34 + 9 = 43.
Notice that −9 inside the bracket becomes +9 outside it.
In simple words: A minus before a bracket flips every sign inside.

Teacher's Note:
1. Check: 52 − 27 = 25 and 52 − 9 = 43.
2. Watch the second sign carefully.

Question 10. Find the value of 60 − 4 × 7 + 36 ÷ 9 by first writing the expression as a sum of its terms. A student answered 28 for this expression. Describe the mistake he is likely to have made.
Answer:
As a sum of terms: 60 − 4 × 7 + 36 ÷ 9 = 60 + (−4 × 7) + (36 ÷ 9).
Terms: 60, −4 × 7 = −28 and 36 ÷ 9 = 4.
Value = 60 − 28 + 4 = 36.
The student probably worked out 60 − (4 × 7 + 36 ÷ 9) = 60 − 32 = 28, so he subtracted the term 36 ÷ 9 instead of adding it.
In simple words: The minus belongs only to 4 × 7, so 36 ÷ 9 is added.

Teacher's Note:
1. The sign belongs to the term right after it.
2. Check the student's answer by trying a wrong bracket.

Question 11. Show that 6 × (9 + 4) = 6 × 9 + 6 × 4 by finding both values. Then use the same idea to find 6 × 97 in a quick way, writing each step.
Answer:
6 × (9 + 4) = 6 × 13 = 78 and 6 × 9 + 6 × 4 = 54 + 24 = 78, so both sides are equal.
Now 97 = 100 − 3, so 6 × 97 = 6 × (100 − 3) = 6 × 100 − 6 × 3 = 600 − 18 = 582.
A multiple of a difference is the difference of the multiples, which makes the work quicker.
In simple words: Break 97 into 100 − 3 and multiply each part by 6.

Teacher's Note:
1. Pick a round number close to 97.
2. This is the distributive property.

Question 12. Whenever Jasoda has to subtract 99 from a number, she subtracts 100 and then adds 1. Use her method to find 456 − 99, and explain with the help of brackets why the method always works.
Answer:
456 − 99 = 456 − 100 + 1 = 356 + 1 = 357.
Why it works: 99 = 100 − 1, so 456 − 99 = 456 − (100 − 1) = 456 − 100 + 1.
The minus before the bracket changes −1 into +1. Taking away 100 removes 1 more than needed, so 1 is added back.
In simple words: Subtracting 100 takes away 1 too many, so add 1 back.

Teacher's Note:
1. Write 99 as 100 − 1.
2. The bracket shows why +1 appears.

Question 13. It is given that 68 − 23 + 45 = 90. Without working out the whole sum again, find the value of each of the following and give a one-line reason.
(i) 69 − 23 + 45
(ii) 68 − 25 + 45
Answer:
Only one term changes each time, so the value changes by the same amount.
(i) 69 − 23 + 45 = 91. The first term is 1 more, so the value is 1 more than 90.
(ii) 68 − 25 + 45 = 88. The term −25 is 2 less than −23, so the value is 2 less than 90.
In simple words: Change in one term = same change in the value.

Teacher's Note:
1. Look at the sign of the term that changed.
2. −25 is smaller than −23.

Question 14. In a garden there are 8 rows of rose plants with 7 plants in each row, and 8 rows of marigold plants with 5 plants in each row. Write two different expressions for the total number of plants and show that both have the same value.
Answer:
Counting the two kinds separately: 8 × 7 + 8 × 5 = 56 + 40 = 96.
Counting row by row: 8 × (7 + 5) = 8 × 12 = 96.
Both give 96 plants. This is the distributive property: a multiple of a sum is the sum of the multiples.
In simple words: Count each kind separately or count 12 plants in each of 8 rows; both give 96.

Teacher's Note:
1. Two ways of counting, one answer.
2. Name the property.

Question 15. Put brackets at the right place in each expression so that it takes the value shown. Write the completed statement and check it.
(i) 45 − 12 + 8 = 25
(ii) 60 − 15 − 5 = 50
Answer:
(i) 45 − (12 + 8) = 25, since 45 − 20 = 25. The bracket makes both 12 and 8 get subtracted.
(ii) 60 − (15 − 5) = 50, since 60 − 10 = 50. The bracket makes 5 get added back after 15 is taken away.
Without brackets the values would be 41 and 40, which are not the ones asked for.
In simple words: Place the bracket so that the right numbers are taken away.

Teacher's Note:
1. Try the bracket and check the value.
2. A minus before a bracket flips signs inside.

Question 16. Without finding the values, decide which of the following expressions are equal to 95 − 41 − 18. Give your reasoning using terms.
(i) 95 − (41 + 18)
(ii) 95 − (41 − 18)
(iii) −41 + 95 − 18
(iv) 96 − 42 − 18
Answer:
The terms of 95 − 41 − 18 are 95, −41 and −18.
(i) Equal. Removing the bracket after the minus gives 95 − 41 − 18, the same terms.
(ii) Not equal. It becomes 95 − 41 + 18, because the sign of −18 changes.
(iii) Equal. It has the same terms, only in a different order.
(iv) Equal. 96 is 1 more than 95 and −42 is 1 less than −41, so the changes cancel.
In simple words: Same terms (or changes that cancel) give the same value.

Teacher's Note:
1. Compare terms, not values.
2. So (i), (iii) and (iv) are equal to it.

Question 17. Evaluate 100 − [30 + (25 − 12)], showing the value of the inner bracket first. Then write the same expression without any brackets and check that both forms give the same value.
Answer:
Inner bracket: 25 − 12 = 13.
Outer bracket: 30 + 13 = 43.
Whole expression: 100 − 43 = 57.
Without brackets: the minus before the outer bracket changes the signs of 30 and of (25 − 12): 100 − 30 − 25 + 12 = 70 − 25 + 12 = 57.
Both forms give 57.
In simple words: Work from the inside out; removing brackets carefully gives the same answer.

Teacher's Note:
1. Inner bracket first.
2. A minus outside flips every sign inside, even inner brackets.

Question 18. Compare the two expressions in each pair using <, > or = by reasoning only. Justify each answer in one sentence.
(i) 47 × (36 − 14) and 47 × 36 − 47 × 14
(ii) 23 + 15 × 9 and (23 + 15) × 9
Answer:
(i) 47 × (36 − 14) = 47 × 36 − 47 × 14, because a multiple of a difference equals the difference of the multiples (distributive property).
(ii) 23 + 15 × 9 < (23 + 15) × 9; on the left only 15 × 9 is added to 23 (giving 158), but on the right the whole 38 is multiplied by 9 (giving 342).
In simple words: See what is being multiplied in each expression.

Teacher's Note:
1. Distributive property gives equal values.
2. Multiplying a bigger amount gives more.

Question 19. Ramesh earns ₹18,000 every month. Each month he spends ₹6,000 on rent, ₹4,500 on food and ₹2,500 on other needs. Write a single expression using brackets for the money he saves in 6 months and find its value.
Answer:
Spending in one month = 6000 + 4500 + 2500.
Saving in 6 months: 6 × [18000 − (6000 + 4500 + 2500)].
6000 + 4500 + 2500 = 13000
18000 − 13000 = 5000
6 × 5000 = 30000
So Ramesh saves ₹30,000 in 6 months.
In simple words: Find the monthly saving, then multiply by 6.

Teacher's Note:
1. Inner bracket is total spending.
2. Square bracket is the monthly saving.

Question 20. Using the numbers 3, 4 and 7 exactly once each, with only the signs + and − and brackets where needed, write three expressions having three different values. Also write the expression that gives the greatest possible value and the one that gives the smallest possible value.
Answer:
Three expressions with different values:
3 + 4 + 7 = 14
7 − 4 + 3 = 6
3 − (4 + 7) = −8
Greatest value: 3 + 4 + 7 = 14, because every number is added.
Smallest value: 3 − (4 + 7) = −8 (same as 3 − 4 − 7), because the smallest number is kept positive and the other two are both subtracted. (Here no sign is placed before the first number.)
In simple words: Add everything for the greatest value; subtract the two bigger numbers from the smallest for the least.

Teacher's Note:
1. Use each number only once.
2. Subtracting the larger numbers makes the value smallest.