Fractions: questions with answers

Both wholes are the same size. Object A is cut into 8 equal parts, so one marked part is $\frac{1}{ 8 }$ of the whole. Object B is cut into 6 equal parts, so one marked part is $\frac{1}{ 6 }$ of the whole. When a whole is cut into fewer equal parts, each part is larger. So the larger marked share is Object B share, which is 1/6 of the whole.

When one whole chocolate bar is divided into 9 equal shares, each person gets one of the 9 equal shares. So one person's share is $\frac{1}{9}$ of the chocolate bar.

The bars show $\frac{12}{8}$ in all. Divide 12 by 8: the quotient is 1 and the remainder is 4, so the mixed number is $1\frac{4}{8}$.

The full shaded amount is $\frac{11}{12}$. The known part is $\frac{9}{12}$. Since the denominators are the same, subtract only the numerators: 11-9=2. So the missing fraction is $\frac{2}{12}$.

The two bars show the same shaded share. The lower bar has 2 times as many equal parts as the top bar, so the shaded-part count also becomes 2 times as large: 2 \$\times$ 2 = 4.

The denominator is the number of equal intervals in one whole unit from 0 to 1. Since the shown unit is divided into 7 equal intervals, the denominator is 7.

The denominator 8 tells us that the unit from 0 to 1 is divided into 8 equal intervals. The numerator 5 tells us to count 5 intervals from 0, so the correct position is the fifth tick after 0.

The strip has 4 equal parts. Since all 4 parts are shaded, the shaded fraction is $\frac{4}{4}$, which is equal to 1 whole.

There are 3 half-units. Each unit counted is $\frac{1}{2}$, so the measured fraction is $\frac{3}{2}$.

The marked part is the difference between the two bar lengths. Subtract $4\frac{1}{2}$ m from $6\frac{3}{4}$ m to get $2\frac{1}{4}$ m.

The fractional part $\frac{2}{5}$ is smaller than $\frac{3}{4}$, so the figure shows one whole of the upper bar as $\frac{20}{20}$. Write both mixed numbers as fractions: $\frac{37}{5}$ and $\frac{19}{4}$. Using Brahmagupta's method, the product of the denominators gives both the same fractional unit: $\frac{148}{20}$ and $\frac{95}{20}$. Subtracting the numerators gives $\frac{148}{20} - \frac{95}{20} = \frac{53}{20}$. As a mixed number, the length that remains is $2\frac{13}{20}$ units.

Both whole chikkis are divided into 4 equal-size parts. One marked part in Chikki A and one marked part in Chikki B each have area equal to 1 out of 4 equal parts of the same-size whole. Their shapes are different, but each marked piece is $\frac{1}{4}$ of a whole chikki.

Each whole uses 8 equal parts. The model has 5 complete wholes and 1 parts left, so it shows $5\frac{1}{8}$.

The denominators are the same, so compare the shaded parts, or numerators. Since 3 is less than 6, the correct symbol is <.

Use the same fractional unit $\frac{1}{24}$ for all three fractions: $\frac{1}{2}=\frac{12}{24}$, $\frac{1}{6}=\frac{4}{24}$ and $\frac{1}{8}=\frac{3}{24}$. Now add only the numerators: $12+4+3=19$. So the total is $\frac{19}{24}$, which matches the example.