Converting Mixed Numbers to Decimals
Converting Mixed Numbers to Decimals is a Grade 7 math skill in Reveal Math Accelerated, Unit 13: Irrational Numbers, Exponents, and Scientific Notation, where students convert the fractional part of a mixed number to a decimal by dividing the numerator by the denominator, then combining with the whole number part. This skill is used to place rational numbers on the number line and to compare them to irrational numbers.
Key Concepts
Property To convert a mixed number to a decimal, you do not need to convert it into an improper fraction. Instead, separate the whole number from the fractional part. The whole number becomes the integer part of the decimal (to the left of the decimal point), and the quotient of the fraction's numerator divided by its denominator becomes the decimal part (to the right of the decimal point).
Examples Example 1: To convert 3 and 1/2 to a decimal, keep the whole number 3. Convert 1/2 to a decimal by dividing 1 by 2, which is 0.5. Combine them to get 3.5. Example 2: To convert 4 and 5/8 to a decimal, keep the whole number 4. Convert 5/8 to a decimal (5 divided by 8), which is 0.625. Combine them to get 4.625. Example 3: To convert 7 and 2/3 to a decimal, keep the 7. Convert 2/3 to a decimal, which is the repeating decimal 0.666... Combine them to get 7.6 with a bar over the 6.
Explanation Mixed numbers are just an addition problem in disguise (for example, 3 and 1/2 is exactly the same as 3 + 1/2). Because of this, you can save time by leaving the whole number exactly as it is. Just use long division to find the decimal identity of the fraction part, and then attach it to the whole number.
Common Questions
How do you convert a mixed number to a decimal?
Keep the whole number part as-is, then divide the numerator of the fraction part by its denominator to get the decimal portion. For example, 2 and 3/4 = 2 + (3 ÷ 4) = 2 + 0.75 = 2.75.
What types of decimals result from converting fractions?
Division of the numerator by the denominator produces either a terminating decimal (like 0.75) or a repeating decimal (like 0.333...). The type depends on whether the denominator has only 2s and 5s as prime factors.
How does converting mixed numbers to decimals help with number comparisons?
Decimals are easier to compare on a number line. Converting all numbers to decimal form lets you order rational and irrational numbers (like pi or square root of 2) by placing them at their approximate positions.
What is Reveal Math Accelerated Unit 13 about?
Unit 13 covers Irrational Numbers, Exponents, and Scientific Notation, including classifying real numbers as rational or irrational, converting between forms, and applying exponent rules.