Step-by-Step (÷/x)
What does each letter in KCF stand for?
Keep, Change, Flip
What is the first step in the following problem?
\frac{2}{3} + \frac{4}{3}
a) Find a common denominator
b) Add 2 and 4 together, keep the denominator the same.
c) KCF
b) Add 2 and 4 together, keep the denominator the same.
(Triple Points) Solve:
2/9 + 4/9
2/9 + 4/9
= \frac{2+4}{9}
=\frac{6}{9}
=\frac{6 \div 3}{9 \div 3}
=\frac{2}{3}
Solve:
\frac{1}{4} \times \frac{2}{3}
\frac{1}{4} \times \frac{2}{3}
= \frac{1 \times 4}{2 \times 3}
= \frac{4}{6}
= \frac{4 \div 2}{6 \div 2}
= \frac{2}{3}
A recipe needs 1/2 cup of sugar. You add another 1/4 cup. What operation finds the total?
Addition
You are combining two amounts together.
(Double Points!) What is the first step of the following problem?
2\frac{1}{2} \times 3\frac{3}{8}
a) Keep Change Flip
b) Multiply straight across
c) Convert the fractions to mixed numbers
c) Convert the fractions to mixed numbers
What is the first step in the following problem.
\frac{5}{6} - \frac{2}{5}
a) KCF
b) Find a common denominator
c) Subtract 2 from 5, keep the denominator the same.
c) Subtract 2 from 5, keep the denominator the same.
7/8 - 2/8
7/8 - 2/8
=\frac{7-2}{8} = \frac{5}{8}
(Triple Points) Solve:
\frac{1}{3} \div \frac{5}{3}
\frac{1}{3} \div \frac{5}{3}
=\frac{1}{3} \times \frac{3}{5}
=\frac{1}{5} Cross Cancel
You have 3/4 of a pizza and you eat 1/3 of it. How pizza was eaten?
Multiplication. You eat PART (1/3) of a WHOLE (the 3/4 of the pizza)
What is the first step of the following problem?
2\frac{1}{2} \div 3\frac{3}{8}
a) Keep Change Flip
b) Divide straight across
c) Convert the fractions to mixed numbers
c) Convert the fractions to mixed numbers
(And then KCF AFTERWARDS)
(Double Points) What do we do with the whole numbers when adding/subtracting mixed numbers.
For example 4 and 3:
4 3/4 - 1 1/5
a) subtract them
b) KCF
c) leave them the way they are
a) Subtract them
Solve:
4/5 + 8/3
4/5 + 8/3
= \frac{4\times3}{5\times3} + \frac{8\times5}{3\times5}
12/15 + 40/15 = \frac{52}{15}
Solve:
3/5 \div 1/2
3/5 \div 1/2
3/5 \times 2/1
=\frac{3\times2}{5\times1}
=\frac{6/5}
A class has 24 students. Two-thirds of them brought lunch. What is the number of students that brought lunch?
Multiplication
24 \times 2/3
OR
2/3 \times 24
You are finding part (students who brought lunch) of a whole (students in the class)
True or False
In this problem, the first step is to do KCF.
\frac{1}{8} \times \frac{2}{7}
FALSE (KCF IS ONLY FOR DIVISION)
Explain how to rewrite 3/4 − 1/6 using a common denominator.
\frac{3xx6}{4xx6}
\frac{1xx4}{6xx4}
18/24 - 4/24
Solve:
2 3/4 + 1/6
2 3/4 + 1/6
= 11/4 + 1/6
= \frac{11\times6}{4\times6} + \frac{1\times4}{6\times4}
= \frac{66}{24} + \frac{4}{24} = \frac{70}{24}
Solve:
\frac{2}{9} \div \frac{4}{3}
\frac{2}{9} \div \frac{4}{3}
=\frac{2}{9} \times \frac{3}{4}
=\frac{2\times3}{9\times4} = \frac{6\div6}{36\div6}=\frac{1}{6}
You have 3/4 liter of juice. There are cups that each hold 1/8 liter of juice. How many cups can be filled?
Division. The 3/4 liter of juice is divided equally among the cups.
\frac{3}{4} \div \frac{1}{8}
Why do we do KCF?
a) Because our teachers told us to
b) Because division means to multiply the reciprocal.
c) So that it's easier to cross cancel.
b) Because division means to multiply the reciprocal.
Why do we need to make sure our fractions have a common denominator before adding or subtracting two fractions?
a) We cannot add or subtract two fractions unless they have a common denominator.
b) Because our teachers told us to.
c) So that it's easier to cross cancel.
a) We cannot add or subtract two fractions unless they have a common denominator.
Solve:
4 6/7 - 1 1/3
\frac{6xx3}{7xx3} and \frac{1xx7}{3xx7}
=\frac{18}{21} - \frac{7}{21}
=\frac{9}{21}
3 1/3 \div 3/4
10/3 \div 3/4
10/3 xx 4/3
40/9
A recipe calls for 3/4 cup of flour. Maya wants to make 3 times as much of the recipe, but she already 1/2 has cup of flour measured out. (2 operations)
Multiplication and Subtraction