Topic 1 Review: Operations with Decimals, Fractions, and Mixed Numbers

Vocabulary and operational concepts covering decimal arithmetic, fraction division, mixed number division, and multistep problem solving from Topic 1.

Product

The answer to a multiplication problem.

Dividend

The quantity to be divided.

Reciprocal

The number used to rewrite a division expression as multiplication by multiplying by the reciprocal of the divisor.

Adding and Subtracting Decimals

Line up the decimal points so that place-value positions correspond, add or subtract as with whole numbers, and place the decimal point in the answer.

Multiplying Decimals

Multiply as with whole numbers, then place the decimal point in the product by starting at the right and counting the number of places equal to the sum of the number of decimal places in each factor.

Dividing Decimals

Multiply the divisor and the dividend by the same power of $10$ so that the divisor is a whole number, place the decimal point in the quotient, and use an algorithm for whole-number division.

Dividing Mixed Numbers

Rename each mixed number as a fraction, rewrite the problem as a multiplication problem using the reciprocal of the divisor, multiply, and rename the fraction quotient as a mixed number.

Multistep Problem Solving Steps

The process to solve multistep problems: decide the steps, choose the correct operations, identify needed information, use information correctly, calculate accurately, and check if the answer is reasonable.