정수와 유리수

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{5\cdot 6-3\cdot 4}{4\cdot 5-2\cdot 3}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{8\cdot 9-7\cdot 6}{5\cdot 6-9\cdot 2}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{{5}^{2}-{3}^{2}}{3-5}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{{6}^{2}-{4}^{2}}{4-6}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{7\cdot 4-2(8-5)}{9\cdot 3-3\cdot 5}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{9\cdot 7-3(12-8)}{8\cdot 7-6\cdot 6}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}$

the quotient of r and the sum of s and 10

the quotient of A and the difference of 3 and B

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

the quotient of the difference of $x\,\text{and}\,y,\,\text{and}\,-3$

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

the quotient of the sum of $m\,\text{and}\,n,\,\text{and}\,4q$

Baking. A recipe for chocolate chip cookies calls for $\frac{3}{4}$ cup brown sugar. Imelda wants to double the recipe. ⓐ How much brown sugar will Imelda need? Show your calculation. ⓑ Measuring cups usually come in sets of $\frac{1}{4},\frac{1}{3},\frac{1}{2},\,\text{and}\,1$ cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the cookie recipe.

Baking. Nina is making 4 pans of fudge to serve after a music recital. For each pan, she needs $\frac{2}{3}$ cup of condensed milk. ⓐ How much condensed milk will Nina need? Show your calculation. ⓑ Measuring cups usually come in sets of $\frac{1}{4},\frac{1}{3},\frac{1}{2},\,\text{and}\,1$ cup. Draw a diagram to show two different ways that Nina could measure the condensed milk needed for $4$ pans of fudge.

Portions Don purchased a bulk package of candy that weighs $5$ pounds. He wants to sell the candy in little bags that hold $\frac{1}{4}$ pound. How many little bags of candy can he fill from the bulk package?

Portions Kristen has $\frac{3}{4}$ yards of ribbon that she wants to cut into $6$ equal parts to make hair ribbons for her daughter’s 6 dolls. How long will each doll’s hair ribbon be?

Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 or 8 slices. Would he prefer 3 out of 6 slices or 4 out of 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 out of 6 slices. Explain what is wrong with Rafael’s reasoning.

Give an example from everyday life that demonstrates how $\frac{1}{2}\cdot \frac{2}{3}\,\text{is}\,\frac{1}{3}.$

Explain how you find the reciprocal of a fraction.

Explain how you find the reciprocal of a negative number.