Covers Unit 9 (Multiply fractions by whole numbers) and Unit 10 (Understand decimals & tenths/hundredths).
The Big Idea: Multiplying a whole number by a fraction is repeated addition: 4 × (1/5) = 1/5 + 1/5 + 1/5 + 1/5 = 4/5.
Multiply the whole number by the numerator. Keep the denominator:
(6 × 1) / 8 = 6/8.
Calculate: 7 × (1/10)
7 × 1 = 7. Denominator stays 10 → 7/10.
The Rule: n × (a/b) = (n × a) / b. Multiply the whole number by the top number only!
Numerator: 5 × 3 = 15. Denominator stays 4.
Improper fraction: 15/4.
Mixed number: 15 ÷ 4 = 3 3/4.
Calculate 4 × (2/3) as an improper fraction and mixed number.
4 × 2 = 8 → 8/3 = 2 2/3.
Word Problem Key: "Each" often signals multiplication: if each batch needs 2/3 cup of milk, 4 batches need 4 × 2/3.
A recipe needs 3/8 pound of butter per batch. How much butter for 6 batches?
6 × (3/8) = 18/8 = 2 2/8 = 2 1/4 pounds.
The Decimal Bridge: The first place after the decimal point is tenths (0.1). The second place is hundredths (0.01).
7/10 = 0.7 (7 tenths)23/100 = 0.23 (23 hundredths)5/100 = 0.05 (5 hundredths; note the placeholder zero in tenths!)Write as decimals: 4/10, 68/100, and 9/100.
4/10 = 0.4 • 68/100 = 0.68 • 9/100 = 0.09.
Rule: You cannot add tenths directly to hundredths! First rename tenths into hundredths by multiplying by 10/10: 3/10 = 30/100.
3/10 = 30/100.
30/100 + 24/100 = 54/100 = 0.54.
Find: 6/10 + 17/100 as both a fraction and a decimal.
60/100 + 17/100 = 77/100 = 0.77.
The Strategy: Always compare place value from left to right. When comparing a tenth to a hundredth, add a trailing zero so both have two digits: 0.4 = 0.40!
0.4 = 0.40 (40 hundredths). 0.29 = 29 hundredths.
Since 40 > 29, 0.4 > 0.29 (even though 29 looks larger than 4!).
Compare using <, >, or =: 0.7 [ ? ] 0.68 and 0.05 [ ? ] 0.5
0.70 > 0.68 → 0.7 > 0.68.
0.05 < 0.50 → 0.05 < 0.5.