Unit 4 Fractions

Multiply and divide mixed number

To multiply or divide mixed numbers, we follow these steps: Write all mixed numbers as improper fractions. Multiply or divide the improper fractions. Write the answer as a mixed number.

when we multiply or divide both the Numerator and denominator by the same nmber

we get equivalent fractions

A fraction is in its lowest terms when the only common factor of the numerator and denominator is.....

1

To reduce a fraction to its lowest terms, you can follow these steps

1. Find the prime factorizations of both the numerator and denominator. 2. Identify all pairs of common prime factors in the numerator and denominator and cancel them out. 3. Multiply the remaining factors in both the numerator and denominator.

Mixed Numbers

A mixed number is a number consisting of a whole number and a proper fraction: 3 3/4 For example, the following numbers are mixed numbers: 2 1/4, 1 1/2, 4 8/9 The value of a mixed number is the sum of the whole number and the fraction: 2 1/3 = 2 +1/3

Adding and subtracting fractions with different denominators

To add or subtract fractions with different denominators, we follow these steps: Find the Least Common Denominator of the fractions. Find the equivalent fractions with this denominator. Add or subtract the new fractions. Reduce the answer to its lowest terms.

Graphing a mixed number

To graph a mixed number, follow these steps: 1. Identify the whole number. 2. Draw a number line containing the whole number and the next greater whole number. 3. Divide the line segment between the whole number and the next greater whole number into equal parts. The number of parts is the same as the denominator of the mixed number. 4. Imagine moving from the whole number to the right and count the parts until the number of parts is the same as the numerator of the mixed number. Then, graph the mixed number.

Graphing a proper fractions

To graph a proper fraction, follow these steps: Draw a number line and mark 0 and 1 Divide the line segment between 0 and 1 into equal parts. The number of parts is the same as the denominator of the fraction. Imagine moving from 0 to the right and count the parts until the number of parts is the same as the numerator of the fraction. Then, graph the fraction.

Subtracting mixed number

To subtract mixed numbers, we follow these steps: Subtract the fractions and reduce the result to its lowest terms. If the minuend is smaller than the subtrahend, "borrow" from the whole number of the minuend. Subtract the whole numbers. Remember to decrease the whole number in the minuend if there was "borrowing". Combine the differences from Steps 1 and 2 to get a mixed number.

Multiplying Fractions

We do the following to multipy two fractions: We multiply the numerators to get the new numerator. We multiply the denominators to get the new denominator. We always reduce the answer to its lowest terms.

Dividing Fraction

When dividing by a fraction, follow these steps: Find the reciprocal of the divisor. Multiply the dividend by the reciprocal of the divisor. Reduce the quotient.

Adding and subtracting fractions with the same denominator

When we add or subtract fractions with the same denominator, we keep this denominator in the answer and only add or subtract the numerators to get the new numerator. We always reduce the answer to its lowest terms.

equivalent fractions

two or more fractions that name the same amount

Imroper and Proper Fraction

Fractions that represent more than 1 whole are called improper fractions. In improper fractions, the numerator is greater than the denominator. For example, the following fractions are improper fractions: 5/4, 9/5, 11/7 Fractions that represent a part of 1 whole are called proper fractions. In proper fractions, the numerator is less than the denominator. For example, the following fractions are proper fractions: 3/4, 1/5, 3/7

Least common Denominator

The Least Common Denominator of two or more fractions is the Least Common Multiple of their denominators. When we compare, add, or subtract fractions with different denominators, we need to find equivalent fractions with a common denominator. The Least Common Denominator is the best choice.

Adding mixed numbers

To add mixed numbers, we follow these steps: Add the fractions and reduce the result to its lowest terms. If the result is an improper fraction, express it as a mixed number. Add the whole numbers. Combine the sums from Steps 1 and 2 to get the answer.