Question 5

Fill in the blanks to make the expressions equal on both sides of the $=$ sign:

(a) $13 + 4 = \underline{\quad} + 6$

(b) $22 + \underline{\quad} = 6 \times 5$

(c) $8 \times \underline{\quad} = 64 \div 2$

(d) $34 - \underline{\quad} = 25$

Arrange the following expressions in ascending (increasing) order of their values.

(a) $67 - 19$

(b) $67 - 20$

(c) $35 + 25$

(d) $5 \times 11$

(e) $120 \div 3$

Find the values of the following expressions by writing the terms in each case.

(a) $28 - 7 + 8$

(b) $39 - 2 \times 6 + 11$

(c) $40 - 10 + 10 + 10$

(d) $48 - 10 \times 2 + 16 \div 2$

(e) $6 \times 3 - 4 \times 8 \times 5$

Write a story/situation for each of the following expressions and find their values.

(a) $89 + 21 - 10$

(b) $5 \times 12 - 6$

(c) $4 \times 9 + 2 \times 6$

Add brackets at appropriate places in the expressions such that they lead to the values indicated.

(a) $34 - 9 + 12 = 13$

(b) $56 - 14 - 8 = 34$

(c) $-22 - 12 + 10 + 22 = -22$

Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality ($=$) equal.

(a) $423 + \underline{\quad\quad} = 419 + \underline{\quad\quad}$

(b) $207 - 68 = 210 - \underline{\quad\quad}$

Using the numbers 2, 3 and 5, and the operators '+' and '-', and brackets, as necessary, generate expressions to give as many different values as possible. For example, $2 - 3 + 5 = 4$ and $3 - (5 - 2) = 0$.

Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it. For example, $36 - 9 = 26 + 1$.

(a) Do you think she always gets the correct answer? Why?

(b) Can you think of other similar strategies? Give some examples.

Consider the two expressions: a) $73 - 14 + 1$, b) $73 - 14 - 1$. For each of these expressions, identify the expressions from the following collection that are equal to it.

(a) $73 - (14 + 1)$

(b) $73 - (14 - 1)$

(c) $73 + (-14 + 1)$

(d) $73 + (-14 - 1)$

Figure it Out

1. Fill in the blanks with numbers, and boxes by signs, so that the expressions on both sides are equal.

(a) $3 \times (6 + 7) = 3 \times 6 + 3 \times 7$

(b) $(8 + 3) \times 4 = 8 \times 4 + 3 \times 4$

(c) $3 \times (5 + 8) = 3 \times 5 \ \Box\ 3 \times \underline{\ \ \ }$

(d) $(9 + 2) \times 4 = 9 \times 4 \ \Box\ 2 \times \underline{\ \ \ }$

(e) $3 \times (\underline{\ \ \ } + 4) = 3 \ \underline{\ \ \ } + \underline{\ \ \ }$

(f) $(\underline{\ \ \ } + 6) \times 4 = 13 \times 4 + \underline{\ \ \ }$

(g) $3 \times (\underline{\ \ \ } + \underline{\ \ \ }) = 3 \times 5 + 3 \times 2$

(h) $(\underline{\ \ \ } + \underline{\ \ \ }) \times \underline{\ \ \ } = 2 \times 4 + 3 \times 4$

(i) $5 \times (9 - 2) = 5 \times 9 - 5 \times \underline{\ \ \ }$

(j) $(5 - 2) \times 7 = 5 \times 7 - 2 \times \underline{\ \ \ }$

(k) $5 \times (8 - 3) = 5 \times 8 \ \Box\ 5 \times \underline{\ \ \ }$

(l) $(8 - 3) \times 7 = 8 \times 7 \ \Box\ 3 \times 7$

(m) $5 \times (12 - \underline{\ \ \ }) = \underline{\ \ \ } \ \Box\ 5 \times \underline{\ \ \ }$

(n) $(15 - \underline{\ \ \ }) \times 7 = \underline{\ \ \ } \ \Box\ 6 \times 7$

(o) $5 \times (\underline{\ \ \ } - \underline{\ \ \ }) = 5 \times 9 - 5 \times 4$

(p) $(\underline{\ \ \ } - \underline{\ \ \ }) \times \underline{\ \ \ } = 17 \times 7 - 9 \times 7$

In the boxes below, fill '<', '>' or '=' after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets to figure this out and not by evaluating the expressions.

(a) $(8 - 3) \times 29 \ \square\ (3 - 8) \times 29$

(b) $15 + 9 \times 18 \ \square\ (15 + 9) \times 18$

(c) $23 \times (17 - 9) \ \square\ 23 \times 17 + 23 \times 9$

(d) $(34 - 28) \times 42 \ \square\ 34 \times 42 - 28 \times 42$

Here is one way to make 14: $2 \times (1 + 6) = 14$. Are there other ways of getting 14? Fill them out below:

(a) $\underline{\quad} \times (\underline{\quad} + \underline{\quad}) = 14$

(b) $\underline{\quad} \times (\underline{\quad} + \underline{\quad}) = 14$

(c) $\underline{\quad} \times (\underline{\quad} + \underline{\quad}) = 14$

(d) $\underline{\quad} \times (\underline{\quad} + \underline{\quad}) = 14$

Find out the sum of the numbers given in each picture below in at least two different ways. Describe how you solved it through expressions.

Read the situations given below. Write appropriate expressions for each of them and find their values.

(a) The district market in Begur operates on all seven days of a week. Rahim supplies 9 kg of mangoes each day from his orchard and Shyam supplies 11 kg of mangoes each day from his orchard to this market. Find the amount of mangoes supplied by them in a week to the local district market.

(b) Binu earns ₹20,000 per month. She spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses every month. What is the amount Binu will save by the end of a year?

(c) During the daytime a snail climbs 3 cm up a post, and during the night while asleep, accidentally slips down by 2 cm. The post is 10 cm high, and a delicious treat is on its top. In how many days will the snail get the treat?

Melvin reads a two-page story every day except on Tuesdays and Saturdays. How many stories would he complete reading in 8 weeks? Which of the expressions below describes this scenario?

(a) $5 \times 2 \times 8$

(b) $(7 - 2) \times 8$

(c) $8 \times 7$

(d) $7 \times 2 \times 8$

(e) $7 \times 5 - 2$

(f) $(7 + 2) \times 8$

(g) $7 \times 8 - 2 \times 8$

(h) $(7 - 5) \times 8$

Find different ways of evaluating the following expressions:

(a) $1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10$

(b) $1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1$

Compare the following pairs of expressions using '$<$', '$>$' or '$=$' or by reasoning.

(a) $49 - 7 + 8 \quad \square \quad 49 - 7 + 8$

(b) $83 \times 42 - 18 \quad \square \quad 83 \times 40 - 18$

(c) $145 - 17 \times 8 \quad \square \quad 145 - 17 \times 6$

(d) $23 \times 48 - 35 \quad \square \quad 23 \times (48 - 35)$

(e) $(16 - 11) \times 12 \quad \square \quad -11 \times 12 + 16 \times 12$

(f) $(76 - 53) \times 88 \quad \square \quad 88 \times (53 - 76)$

(g) $25 \times (42 + 16) \quad \square \quad 25 \times (43 + 15)$

(h) $36 \times (28 - 16) \quad \square \quad 35 \times (27 - 15)$

Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets. There can be more than one expression which is equal to the given expression.

(a) $83 - 37 - 12$

(i) $84 - 38 - 12$

(ii) $84 - (37 + 12)$

(iii) $83 - 38 - 13$

(iv) $-37 + 83 - 12$

(b) $93 + 37 \times 44 + 76$

(i) $37 + 93 \times 44 + 76$

(ii) $93 + 37 \times 76 + 44$

(iii) $(93 + 37) \times (44 + 76)$

(iv) $37 \times 44 + 93 + 76$

Choose a number and create ten different expressions having that value.