In each of the figures given below, find the fraction of the big square. Class 7

In each of the figures given below, find the fraction of the big square. Class 7

Question 1.

In each of the figures given below, find the fraction of the big square that the shaded region occupies. Class 7

Solution:

(i) This square has been divided now into eight triangles of equal size.

The shaded portion has three such triangles (6, 7 and 8).

So, these shaded region occupies the [latex]\frac {3}{8}[/latex] fraction of the big square.

(ii) The big square has been divided into 8 × 4 = 32 small triangles. Out of these, the shaded regions consists of two such small triangles.

So, shaded region is [latex]\frac {2}{32}[/latex], i.e., [latex]\frac {1}{16}[/latex] fraction of the big square.

Question 2.

Evaluate the following: Class 7

Solution:

3 ÷ [latex]\frac {7}{9}[/latex] = 3 × [latex]\frac {9}{7}[/latex] = [latex]\frac{3 \times 9}{7}[/latex] = [latex]\frac {27}{7}[/latex]

[latex]\frac {14}{4}[/latex] ÷ 2 = [latex]\frac {14}{4}[/latex] × [latex]\frac {1}{2}[/latex] = [latex]\frac {14}{8}[/latex] = [latex]\frac {7}{2}[/latex]

[latex]\frac {2}{3}[/latex] ÷ [latex]\frac {7}{3}[/latex] = [latex]\frac {2}{3}[/latex] × [latex]\frac {3}{2}[/latex] = [latex]\frac{2 \times 3}{3 \times 2}[/latex] = [latex]\frac {6}{6}[/latex] = 1

[latex]\frac {14}{6}[/latex] ÷ [latex]\frac {7}{3}[/latex] = [latex]\frac {14}{6}[/latex] × [latex]\frac {3}{7}[/latex] = [latex]\frac{14 \times 3}{6 \times 7}[/latex] = 1

[latex]\frac {4}{3}[/latex] ÷ [latex]\frac {3}{4}[/latex] = [latex]\frac {4}{3}[/latex] × [latex]\frac {4}{3}[/latex] = [latex]\frac{4 \times 4}{3 \times 3}[/latex] = [latex]\frac {16}{9}[/latex]

[latex]\frac {7}{4}[/latex] ÷ [latex]\frac {1}{7}[/latex] = [latex]\frac {7}{4}[/latex] × [latex]\frac {7}{1}[/latex] = [latex]\frac{7 \times 7}{4}[/latex] = [latex]\frac {49}{4}[/latex]

[latex]\frac {8}{2}[/latex] ÷ [latex]\frac {4}{15}[/latex] = [latex]\frac {8}{2}[/latex] × [latex]\frac {15}{4}[/latex] = [latex]\frac{8 \times 15}{2 \times 4}[/latex] = [latex]\frac{8 \times 15}{8}[/latex] = 15

[latex]\frac {1}{5}[/latex] ÷ [latex]\frac {1}{9}[/latex] = [latex]\frac {1}{5}[/latex] × [latex]\frac {9}{1}[/latex] = [latex]\frac{1 \times 9}{5 \times 1}[/latex] = [latex]\frac {9}{5}[/latex]

[latex]\frac {1}{6}[/latex] ÷ [latex]\frac {11}{12}[/latex] = [latex]\frac {1}{6}[/latex] × [latex]\frac {12}{11}[/latex] = [latex]\frac{1 \times 12}{6 \times 11}[/latex] = [latex]\frac {2}{11}[/latex]

3[latex]\frac {2}{3}[/latex] ÷ 1[latex]\frac {3}{8}[/latex] = [latex]\frac {11}{3}[/latex] ÷ [latex]\frac {11}{8}[/latex] = [latex]\frac {11}{3}[/latex] × [latex]\frac {8}{11}[/latex] = [latex]\frac{11 \times 8}{3 \times 11}[/latex] = [latex]\frac {8}{3}[/latex]