Arithmetic Chapter 5 Multiplication And Division Of A Number And By Fraction
Arithmetic Chapter 5 the Rule Of Multiplication Of A Fraction By Whole Number
1. Multiplication of a proper fraction by the whole number
- We know that 2/7 is a proper fraction (v the numerator < the denomination).
- Suppose we have to multiply this proper fraction by any whole number say 7.
- So the mathematical problem is 2/7 x 7 = What is the value?
- Here the rule is:
A proper fraction x the whole number = \(\frac{The number of the proper fraction x whole number}{The denominator of the proper fraction}\)
According to the above rule, \(\frac{2}{7} \times 7\)
= 2
1. Similarly \(\frac{5}{6} \times 8\)
= \(\frac{5 \times 8}{6}\)
= \(\frac{5 \times 4}{3}\)
= 20/3
= \(6 \frac{2}{3}\)
\(\frac{5}{6} \times 8\) = \(6 \frac{2}{3}\)
WBBSE Class 6 Multiplication and Division Notes
2. similarly \(\frac{11}{14} \times 21\)
= \(\frac{11}{14} \times 21\)
= \(\frac{11 \times 21}{14}\)
= \(\frac{11 \times 3}{2}\)
= 33/2
= \(16 \frac{1}{2}\)
\(\frac{11}{14} \times 21\) = \(16 \frac{1}{2}\)
3. similarly \(\frac{17}{25} \times 35\)
= \(\frac{17}{25} \times 35\)
= \(\frac{17 \times 35}{25}\)
= \(\frac{17 \times 7}{5}\)
= 119/5
= \(23 \frac{4}{5}\)
\(\frac{17}{25} \times 35\) = \(23 \frac{4}{5}\)
Understanding Multiplication of Fractions
2. Multiplication of an improper fraction by the whole number :
- We know that “ is an improper fraction (v the numerator > the denominator).
- Suppose we have to multiply this improper fraction by any whole number say 15.
- So the mathematical problem is:
Here also the rule is: The fraction x whole number = \(\frac{The numerator of the fraction x whole number}{The denominator of the fraction}\)
According to the above rule,
= \(\frac{8}{5} \times 15\)
= \(\frac{8 \times 15}{5}\)
= 8 x 3
= 24
Short Questions on Division of Fractions
1. Similarly \(\frac{11}{7} \times 4\)
= \(\frac{11}{7} \times 4\)
= \(\frac{11 \times 4}{7}\)
= 44/7
= \(4 \frac{2}{7}\)
\(\frac{11}{7} \times 4\) = \(4 \frac{2}{7}\)
2. Similarly \(\frac{15}{4} \times 9\)
= \(\frac{15}{4} \times 9\)
= \(\frac{15 \times 9}{4}\)
= 135/2
= \(33 \frac{3}{4}\)
\(\frac{15}{4} \times 9\) = \(33 \frac{3}{4}\)
3. Similarly \(\frac{24}{8} \times 14\)
= \(\frac{24}{8} \times 14\)
= \(\frac{21 \times 14}{8}\)
= 147/4
= \(36 \frac{3}{4}\)
\(\frac{24}{8} \times 14\) = \(36 \frac{3}{4}\)
Common Questions About Multiplying Fractions
3. Multiplication of a mixed fraction or a complex fraction by a whole number :
- To multiply a mixed fraction or a complex fraction by a whole number, first, we have to convert the given fraction to the improper fraction and then according to the rule of 5.1.B.
- The multiplication is to be completed.
1. For Example \(5 \frac{1}{3} \times 7\)
= \(5 \frac{1}{3} \times 7\)
= \(\frac{16}{3} \times 7\)
= \(\frac{16 \times 7}{3}\)
= 112/3
= \(37 \frac{1}{3}\)
\(5 \frac{1}{3} \times 7\) = \(37 \frac{1}{3}\)
2. For Example \(7 \frac{1}{2} \times 12\)
= \(7 \frac{1}{2} \times 12\)
= \(\frac{15}{2} \times 12\)
= \(\frac{15 \times 12}{2}\)
= 15 x 6
= 90
\(7 \frac{1}{2} \times 12\) = 90
Practice Problems on Fraction Multiplication and Division
3. For Example \(\frac{\frac{3}{4}}{\frac{5}{7}} \times 14\)
= \(\frac{\frac{3}{4}}{\frac{5}{7}} \times 14\)
= \(\left(\frac{3}{4} \times \frac{7}{5}\right) \times 14\)
= \(\frac{21}{20} \times 14\)
= \(\frac{21 \times 14}{20}\)
= \(\frac{21 \times 7}{10}\)
= 147/10
= \(14 \frac{7}{10}\)
\(\frac{\frac{3}{4}}{\frac{5}{7}} \times 14\) = \(14 \frac{7}{10}\)