DCA 2 Review

Front

What is an equivalent expression?

Back

An equivalent expression is one that has the same value as another expression for all values of the variable(s) involved. For example, 9(6 + x) is equivalent to 9⋅6 + 9⋅x.

Front

How do you find the amount of paint needed to make a larger quantity of a mixture?

Back

To find the amount of paint needed for a larger quantity, set up a proportion based on the original mixture. For example, if 5 pints of blue and 2 pints of yellow make 7 pints of green, to make 28 pints, you would calculate: (5/7) * 28 = 20 pints of blue.

Front

What is the formula to calculate a percentage of a total?

Back

To calculate a percentage of a total, use the formula: (percentage/100) * total. For example, to find 32% of a budget, multiply the budget by 0.32.

Front

How do you convert a percentage to a fraction?

Back

To convert a percentage to a fraction, divide the percentage by 100 and simplify if possible. For example, 32% = 32/100 = 8/25.

Front

What is the relationship between fractions and percentages?

Back

Fractions and percentages are two ways to represent parts of a whole. A percentage is a fraction with a denominator of 100.

Front

How do you calculate the number of people wearing a specific shirt based on a percentage?

Back

To calculate the number of people wearing a specific shirt based on a percentage, multiply the total number of people by the percentage (as a decimal). For example, 75% of 120 people is 0.75 * 120 = 90 people.

Front

What does it mean to simplify a fraction?

Back

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you solve for a variable in an equation?

Back

To solve for a variable, isolate the variable on one side of the equation using inverse operations. For example, in the equation x + 3 = 7, subtract 3 from both sides to find x = 4.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.