HSPT Math - How to multiply and divide fractions

$\frac{4}{5}*\frac{2}{3}=$

$\frac{8}{15}$

$\frac{6}{8}$

$\frac{6}{15}$

$\frac{8}{8}$

Explanation

Multiply the numerators then denominators:

$\frac{4}{5}* \frac{2}{3}=\frac{8}{15}$

Answer: $\frac{8}{15}$

Multiply:

$0.58 \times 8.3$

Explanation

First, multiply the numbers, ignoring the decimal points:

$58 \times 83 = 4814$

Since the two factors in the original product have three digits to the right of the decimal points between them, position the decimal point in the product such that three digits are at its right. The result, therefore, is

The gas tank in Renee's mustang is filled to capacity at $13\frac{1}{2}$ gallons. She used $\frac{2}{3}$ of a tank of gas to take a drive to the shore. How much gas did it take to drive to the shore?

gallons

$8 \frac{1}{2}$ gallons

$9 \frac{1}{2}$ gallons

Explanation

To solve this word problem, multiply the fractions. First convert any mixed number to an improper fraction:

$13\frac{1}{2} = \frac{(2\times13 )+1}{2} = \frac{27}{2}$

Next, multiply the numerators and the denominators of both improper fractions.

$\frac{27}{2} \times\frac{2}{3} = \frac{54}{6} = 9$

gallons of gas was consumed on Renee's trip to the shore.

$-\frac{5}{6 }\times \frac{3}{5}$

$-\frac{1}{2}$

$-\frac{1}{6}$

$\frac{7}{11}$

$-\frac{5}{6}$

Explanation

The formula for multiplication of fractions is:

$\frac{a}{b\ }\times \frac{c}{d} =\frac{ac}{bd}$

Where and It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

$-\frac{5}{6\ }\times \frac{3}{5} =\frac{-5\times 3}{6\times 5}$

$\frac{-5\times 3}{6\times 5} = -\frac{15}{30}$ A negative times a positive is a negative.

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 15.

$-\frac{15\div 15}{30\div 15} =-\frac{1}{2}$

Simplify the expression.

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

$\frac{3}{16}$

$\frac{1}{8}$

$\frac{5}{12}$

$\frac{5}{16}$

Explanation

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

Start with the terms in parentheses, using the order of operations. Find the least common denominator.

$\left ( {\frac{1* 2}{2* 2} + \frac{1}{4}}\right ) *\left ({\frac{1* 2}{2*2} - \frac{1}{4}}\right )$

$\left ( {\frac{2}{4} + \frac{1}{4}}\right ) * \left ({\frac{ 2}{4} - \frac{1}{4}}\right )$

Add the fractions in parentheses.

$\left ( {\frac{2+1}{4} } \right ) * \left ({\frac{2-1}{4} } \right )$

Multiply the fractions and simplify.

${\frac{3}{4} } *{\frac{1}{4} } = \frac{3 * 1}{4 * 4} = \frac{3}{16}$

Evaluate:

$8\frac{1}{3}\div \frac{1}{6}$

$\frac{50}{3}$

$\frac{50}{6}$

Explanation

A mixed number represents the sum of an integer and a fraction. In order to evaluate this problem first we need to change the mixed number ( $8\frac{1}{3}$ ) to an improper fraction. Improper fractions are fractions whose numerator is greater than the denominator. So we can write:

$8\frac{1}{3}=\frac{8\times 3+1}{3}=\frac{25}{3}$

Now we should evaluate $\frac{25}{3}\div \frac{1}{6}$ and we have:

$\frac{25}{3}\div \frac{1}{6}=\frac{25}{3}\times \frac{6}{1}=50$

$\frac{7}{16}*\frac{8}{3}=?$

$\frac{7}{6}$

$\frac{15}{19}$

$\frac{56}{19}$

$\frac{6}{7}$

Explanation

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

So $\frac{(7*8)}{(16*3)}$

Then simplify the answer by dividing by the greatest common factor. $\frac{(56/8)}{(48/8)}$

After performing this the answer is $\frac{7}{6}$ .

One of Floyd's World Famous Ooey Gooey Butter Cakes requires two and one-half cups of flour and four eggs, among other ingredients.

Floyd wants to make seven of these cakes for a wedding. He has sixteen cups of flour on hand as well as three dozen eggs. Assuming he has enough of all other ingredients, can Floyd make the seven cakes he wants to make?

No, because he does not have enough flour.

No, because he does not have enough eggs.

No, because he does not have enough flour or enough eggs.

Yes.

Explanation

In order to make seven butter cakes, Floyd must use

$4 \times 7 = 28$ eggs.

Floyd has three dozen, or 36, eggs on hand, so he has enough eggs.

Floyd must use

$2 \frac{1}{2} \times 7 = \frac{5}{2} \times \frac{7}{1} = \frac{35}{2} = 17 \frac{1}{2}$ cups of flour.

Floyd has 16 cups on hand, so he does not have enough flour.

A tree feet high casts a shadow 20 feet long at the same time a tree 30 feet high casts a shadow how many feet long? Give your answer in terms of .

$\frac{600}{M}$

$\frac{M}{600}$

$\frac{20M}{30}$

$\frac{30M}{20}$

Explanation

The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be :