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Fractions and Decimals

    Exercise 2.1

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7th class > Fractions and Decimals > Exercise 2.1

Exercise 2.1

1.Which of the drawings (a) to (d) show :

(i)2x15 (ii)2x12 (iii)3x23 (iv)3x14 (v)6x15

matches with

matches with

matches with

matches with

2. Some pictures (a) to (c) are given below. Tell which of them show:

(i)3x15=35 (ii)2x13=23 (iii)3x34=214 (iv)3x12=32

matches with

matches with

matches with

3. Multiply and reduce to lowest form and convert into a mixed fraction:

Instruction

(i) 7 × 35 = 7×35=
Convert to Mixed Fraction: 21 ÷ 5 = with remainder
Thus, 215 = 4 ×
(ii) 4 × 13 = 4×13 =
Convert to Mixed Fraction: 4 ÷ 3 = with remainder
Thus, 43 = ×
(iii) 2 × 67 = 2×67 =
Convert to Mixed Fraction: 12 ÷ 7 = with remainder
Thus, 127 = ×
(iv) 5 × 29 = 5×29 =
Convert to Mixed Fraction: 10 ÷ 9 = with remainder
Thus, 109 = ×
(v) 23× 4 = 2×43 =
Convert to Mixed Fraction: 8 ÷ 3 = with remainder
Thus, 83 = ×
(vi) 52× 6 = = 5×62 = =
(vii) 11 × 47 = 11×47 =
Convert to Mixed Fraction: 44 ÷ 7 = with remainder .
Thus, 447 = ×
(viii) 20 × 45 = 20×45= =
(ix) 13 × 13 = 13×13 =
Convert to Mixed Fraction: 13 ÷ 3 = with remainder
Thus, 133 = ×
(x) 15 × 35 = 15×35 =

4. Write the fraction for the given diagram representation:

Instruction

Write the fraction for the blue coloured circles in the given picture (next slide)
Blue coloured circles =
Write the fraction for the green coloured triangles in the given picture (next slide)
Green coloured triangles =
Write the fraction for the blue coloured squares in the given picture (next slide)
Blue coloured squares =

5. Find:

Instruction

(1) 12 of (i) 24 (ii) 46
(i) 12 × 24 = 242 =
(ii) 12 × 46 = 462 =
(2) 23 of (i) 18 (ii) 27
(i) 23 × 18 = 2×183 =
(i) 23 × 27 = 2×273 =
__{.m-red}(3) 34 of (i) 16 (ii) 36__s
(i) 34 × 16 = 3×164 =
(ii) 34 × 36 = 3×364 =
(4) 45 of (i) 20 (ii) 35
(i) 20 × 45 = 805 =
(ii) 35 × 45 = 1405 =

6. Multiply and express as a mixed fraction :

Instruction

(a)3 × 515
Converting to improper fraction: 3 × =
Converting back to mixed fraction: 785 = ×
(b)5 × 634
Converting to improper fraction: 5 × =
Converting back to mixed fraction: 1354 = ×
(c) 7 × 2 14
Converting to improper fraction: 7 × =
Converting back to mixed fraction: 634 = ×
(d) 4 × 6 13
Converting to improper fraction: 4 × =
Converting back to mixed fraction: 763 = ×
(e) 314 × 6
Converting to improper fraction: × 6 =
Converting back to mixed fraction: 784 = ×
(f) 3 25 × 8
Converting to improper fraction: × 8 =
Converting back to mixed fraction: 1365 = ×

7.Find:

Instruction

(a) 12 of (i) 234 (ii) 429
(i) 12 × 234 = 12 × (Convert to improper fraction) =
Converting back to mixed fraction: 118 = ×
(ii) 12 × 429 = 12 × (Convert to improper fraction) =
Converting back to mixed fraction: 3818 = ×
(b) 58 of (i) 3 56 (ii) 9 23
(i) 58 × 356 = 58 × (Convert to improper fraction) =
Converting back to mixed fraction: 11548 = ×
(ii) 58 × 923 = 58 × (Convert to improper fraction) =
Converting back to mixed fraction: 14524 = ×

8. Vidya and Pratap went for a picnic. Their mother gave them a water bottle thatcontained 5 litres of water. Vidya consumed 25 of the water. Pratap consumed the remaining water.

(i) How much water did Vidya drink?

(ii) What fraction of the total quantity of water did Pratap drink?

Solution:

  1. Vidya drank 25 of the water.

  2. We need to find how much water Vidya drank.

  3. We need to determine the fraction of water Pratap drank.

(i) Calculate 25 of 5 liters:

25 × 5 = 2×55 =105 = liters.

Therefore, Vidya drank 2 liters of water.

(ii) Calculate the fraction of water Pratap drank:

Fraction = AmountPratapdrankTotalamount =3liters5liters = .

Therefore, Pratap drank 35 of the total water.