Compare the following fractions. For some, you may need to make the denominators the same first.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your fraction problems.

.9

1. Fill in the $<$ or $>$ symbol:

a) $\frac{3}{4}$ $<$ $\frac{6}{4}$
b) $\frac{9}{10}$ $>$ $\frac{7}{10}$
c) $\frac{11}{100}$ $<$ $\frac{17}{100}$
d) $\frac{99}{100}$ $>$ $\frac{89}{100}$

2. First make sure the fractions have the same denominator and then compare them by filling in $<$ or $>$ or $=$ symbols:

a) $\frac{4}{5}$ ___ $\frac{9}{10}$

Convert $\frac{4}{5}$ to have a denominator of 10.
$$ \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} $$
Compare $\frac{8}{10}$ and $\frac{9}{10}$ .
$$ \frac{8}{10} < \frac{9}{10} $$ So, $\boxed{\frac{4}{5} < \frac{9}{10}}$
- b) $\frac{3}{2}$ ___ $\frac{5}{16}$
Convert $\frac{3}{2}$ to have a denominator of 16.
$$ \frac{3}{2} = \frac{3 \times 8}{2 \times 8} = \frac{24}{16} $$
Compare $\frac{24}{16}$ and $\frac{5}{16}$ .
$$ \frac{24}{16} > \frac{5}{16} $$ So, $\boxed{\frac{3}{2} > \frac{5}{16}}$
- c) $\frac{5}{6}$ ___ $\frac{11}{12}$
Convert $\frac{5}{6}$ to have a denominator of 12.
$$ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} $$
Compare $\frac{10}{12}$ and $\frac{11}{12}$ .
$$ \frac{10}{12} < \frac{11}{12} $$ So, $\boxed{\frac{5}{6} < \frac{11}{12}}$
- d) $\frac{13}{18}$ ___ $\frac{2}{3}$
Convert $\frac{2}{3}$ to have a denominator of 18.
$$ \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} $$
Compare $\frac{13}{18}$ and $\frac{12}{18}$ .
$$ \frac{13}{18} > \frac{12}{18} $$ So, $\boxed{\frac{13}{18} > \frac{2}{3}}$
- e) $\frac{9}{21}$ ___ $\frac{3}{7}$

Simplify $\frac{9}{21}$ .

$$
\frac{9}{21} = \frac{9 \div 3}{21 \div 3} = \frac{3}{7}
$$

Compare $\frac{3}{7}$ and $\frac{3}{7}$ .
$$ \frac{3}{7} = \frac{3}{7} $$ So, $\boxed{\frac{9}{21} = \frac{3}{7}}$
- f) $\frac{6}{11}$ ___ $\frac{12}{55}$
Convert $\frac{6}{11}$ to have a denominator of 55.
$$ \frac{6}{11} = \frac{6 \times 5}{11 \times 5} = \frac{30}{55} $$
Compare $\frac{30}{55}$ and $\frac{12}{55}$ .
$$ \frac{30}{55} > \frac{12}{55} $$ So, $\boxed{\frac{6}{11} > \frac{12}{55}}$
3. Arrange these fractions in descending order, by first writing them all with a denominator of 48:
The fractions are: $\frac{5}{6}, \frac{1}{3}, \frac{11}{12}, \frac{19}{24}, \frac{3}{4}, \frac{7}{8}, \frac{11}{24}, \frac{12}{24}$ .
Convert each fraction to have a denominator of 48.
$\frac{5}{6} = \frac{5 \times 8}{6 \times 8} = \frac{40}{48}$ $\frac{1}{3} = \frac{1 \times 16}{3 \times 16} = \frac{16}{48}$ $\frac{11}{12} = \frac{11 \times 4}{12 \times 4} = \frac{44}{48}$ $\frac{19}{24} = \frac{19 \times 2}{24 \times 2} = \frac{38}{48}$ $\frac{3}{4} = \frac{3 \times 12}{4 \times 12} = \frac{36}{48}$ $\frac{7}{8} = \frac{7 \times 6}{8 \times 6} = \frac{42}{48}$ $\frac{11}{24} = \frac{11 \times 2}{24 \times 2} = \frac{22}{48}$ $\frac{12}{24} = \frac{12 \times 2}{24 \times 2} = \frac{24}{48}$
Arrange the fractions with denominator 48 in descending order (largest to smallest).
$\frac{44}{48}, \frac{42}{48}, \frac{40}{48}, \frac{38}{48}, \frac{36}{48}, \frac{24}{48}, \frac{22}{48}, \frac{16}{48}$
Write the original fractions in descending order.
$\boxed{\frac{11}{12}, \frac{7}{8}, \frac{5}{6}, \frac{19}{24}, \frac{3}{4}, \frac{12}{24}, \frac{11}{24}, \frac{1}{3}}$
.11

1. There are 600 people in a concert audience. $\frac{3}{10}$ are male and 45% are older than 10 years of age.
The question is incomplete, but I can calculate the number of males and the number of people older than 10 years.
Calculate the number of males.
$\text{Number of males} = \frac{3}{10} \times 600$ $\text{Number of males} = 3 \times 60 = 180$
There are 180 males.
Calculate the number of people older than 10 years of age.
$\text{Number of people older than 10} = 45\% \text{ of } 600$ $\text{Number of people older than 10} = \frac{45}{100} \times 600$ $\text{Number of people older than 10} = 45 \times 6 = 270$
There are 270 people older than 10 years of age.

Compare the following fractions. For some, you may need to make the denominators the same first.

Step-by-step solution

Convert $\frac{4}{5}$ to have a denominator of 10.

Compare $\frac{8}{10}$ and $\frac{9}{10}$ .

Convert $\frac{3}{2}$ to have a denominator of 16.

Compare $\frac{24}{16}$ and $\frac{5}{16}$ .

Convert $\frac{5}{6}$ to have a denominator of 12.

Compare $\frac{10}{12}$ and $\frac{11}{12}$ .

Convert $\frac{2}{3}$ to have a denominator of 18.

Compare $\frac{13}{18}$ and $\frac{12}{18}$ .

Simplify $\frac{9}{21}$ .

Compare $\frac{3}{7}$ and $\frac{3}{7}$ .

Convert $\frac{6}{11}$ to have a denominator of 55.

Compare $\frac{30}{55}$ and $\frac{12}{55}$ .

Convert each fraction to have a denominator of 48.

Arrange the fractions with denominator 48 in descending order (largest to smallest).

Write the original fractions in descending order.

Calculate the number of males.

Calculate the number of people older than 10 years of age.

Still stuck on this one?

More Mathematics Questions

Compare the following fractions. For some, you may need to make the denominators the same first.

Step-by-step solution

Convert 45\frac{4}{5}54​ to have a denominator of 10.

Compare 810\frac{8}{10}108​ and 910\frac{9}{10}109​.

Convert 32\frac{3}{2}23​ to have a denominator of 16.

Compare 2416\frac{24}{16}1624​ and 516\frac{5}{16}165​.

Convert 56\frac{5}{6}65​ to have a denominator of 12.

Compare 1012\frac{10}{12}1210​ and 1112\frac{11}{12}1211​.

Convert 23\frac{2}{3}32​ to have a denominator of 18.

Compare 1318\frac{13}{18}1813​ and 1218\frac{12}{18}1812​.

Simplify 921\frac{9}{21}219​.

Compare 37\frac{3}{7}73​ and 37\frac{3}{7}73​.

Convert 611\frac{6}{11}116​ to have a denominator of 55.

Compare 3055\frac{30}{55}5530​ and 1255\frac{12}{55}5512​.

Convert each fraction to have a denominator of 48.

Arrange the fractions with denominator 48 in descending order (largest to smallest).

Write the original fractions in descending order.

Calculate the number of males.

Calculate the number of people older than 10 years of age.

Still stuck on this one?

More Mathematics Questions

Convert $\frac{4}{5}$ to have a denominator of 10.

Compare $\frac{8}{10}$ and $\frac{9}{10}$ .

Convert $\frac{3}{2}$ to have a denominator of 16.

Compare $\frac{24}{16}$ and $\frac{5}{16}$ .

Convert $\frac{5}{6}$ to have a denominator of 12.

Compare $\frac{10}{12}$ and $\frac{11}{12}$ .

Convert $\frac{2}{3}$ to have a denominator of 18.

Compare $\frac{13}{18}$ and $\frac{12}{18}$ .

Simplify $\frac{9}{21}$ .

Compare $\frac{3}{7}$ and $\frac{3}{7}$ .

Convert $\frac{6}{11}$ to have a denominator of 55.

Compare $\frac{30}{55}$ and $\frac{12}{55}$ .