Dividing Mixed Numbers
Dividing mixed numbers in Grade 8 Saxon Math Course 3 requires converting mixed numbers to improper fractions and then multiplying by the reciprocal of the divisor. Students apply the keep-change-flip method (keep the first fraction, change division to multiplication, flip the second fraction) and simplify results. This skill is applied in proportional reasoning and real-world measurement division.
Key Concepts
Property First, convert all mixed numbers to improper fractions. Then, instead of dividing, multiply the first fraction by the reciprocal (the flipped version) of the second fraction. Simplify the result.
Examples $$4\frac{1}{2} \div 1\frac{1}{2} \rightarrow \frac{9}{2} \div \frac{3}{2} = \frac{9}{2} \times \frac{2}{3} = \frac{18}{6} = 3$$ $$3\frac{1}{3} \div 1\frac{2}{3} \rightarrow \frac{10}{3} \div \frac{5}{3} = \frac{\cancel{10}^2}{3} \times \frac{3}{\cancel{5} 1} = \frac{2 \times 3}{3 \times 1} = 2$$.
Explanation Dividing mixed numbers has a cool secret: don't divide, multiply! First, turn your mixed numbers into improper fractions. Then, take the second fraction, flip it upside down (this is its reciprocal), and multiply instead. It’s the classic 'keep, change, flip' move that turns a tricky division problem into a much simpler multiplication one.
Common Questions
How do you divide mixed numbers?
Convert both mixed numbers to improper fractions. Apply the keep-change-flip rule: keep the first fraction, change division to multiplication, flip (take reciprocal of) the second fraction. Then multiply and simplify.
What is the keep-change-flip rule?
Keep-change-flip is a memory device for fraction division: Keep the first fraction unchanged, Change the division sign to multiplication, Flip the second fraction (write its reciprocal). Then multiply.
How do you divide 2 1/2 by 1 1/4?
Convert: 5/2 divided by 5/4. Keep: 5/2. Change to multiply. Flip: x 4/5. Result: (5 x 4)/(2 x 5) = 20/10 = 2.
How do you convert a mixed number to an improper fraction for division?
Multiply the whole number by the denominator and add the numerator. This sum becomes the new numerator over the original denominator. For example, 3 2/5 = 17/5.
How does Saxon Math Course 3 teach dividing mixed numbers?
Saxon Math Course 3 teaches the convert-then-divide method consistently, applying it to word problems involving partitioning measurements, sharing quantities, and scale calculations.