Tenths and Hundredths: Same Amount, New Name

Lesson 1 of 1: Fractions and Decimal Foundations

In this lesson:

• Rewrite a tenths fraction as a hundredths fraction
• Add a tenths fraction and a hundredths fraction

Your Learning Objectives for Today

By the end of today, you can:

1. Rewrite a tenths fraction as a hundredths fraction
2. Explain why multiplying by 10 works, with a grid
3. Add a tenths fraction and a hundredths fraction
4. Use a grid to check an addition
5. Apply this to money and measurement

Dimes, Pennies, and the Same Amount

• Maria has 3 dimes.
• Jamal has 30 pennies.
• Do they have the same amount of money?

Recall: How Equivalent Fractions Work

• Give a fraction equal to .
• What did you do to the top? To the bottom?
• Rule: multiply both by the same number.

Let's Count This New Grid

100 small squares, arranged in 10 columns.

One Column Equals Two Names

One shaded column: .

Three Columns, Two More Names

Three shaded columns: .

Why the Rule Works Every Time

• Multiply the numerator and the denominator by 10.

• The "same number" is always 10, because 10 × 10 = 100.

A Few More Conversions, Same Pattern

• Watch out: special to tenths and hundredths, since 10 × 10 = 100 — not for fractions like thirds and fifths.

Predict First: 3/10 or 3/100?

• A student says .
• Look at the grid: 30 shaded squares vs. only 3 shaded squares.
• Are these really the same amount?
• Predict before you check the picture.

Your Turn: Convert Both Directions

Pause and try both before checking your answers.

Can We Add These Directly?

• The pieces are different sizes.
• What do we need before we can add them?

Convert, Then Add the Parts

Step 1: Convert the tenths fraction.

Step 2: Add the numerators; the denominator stays 100.

The Picture Matches the Math

34 of 100 squares shaded: 30 from , 4 from .

Predict First: Is This Right?

• A classmate says (added the tops, then added the bottoms).
• Our grid has 100 squares total.
• Could the answer really have 110 parts?

Another Example: Convert and Add

Step 1: Convert.

Step 2: Add.

Read the Picture, Find the Sum

How many squares are shaded, all together?

When Hundredths Is the Bigger Part

Step 1: Convert.

Step 2: Add.

• The steps are exactly the same, no matter which part is bigger.

When the Sum Is One Whole

Step 1: Convert.

Step 2: Add.

• is exactly one whole — a normal, legitimate answer.

Work Backward: Find the Addends

• The sum is .
• Find a tenths fraction and a hundredths fraction that add to it.
• Write your own pair alone, then compare with a neighbor.

Solve It Completely On Your Own

• No grid. No fill-in-the-blank. Show every step.

Time to See This in Real Life

• You can convert tenths to hundredths.
• You can add them together.
• Now: money and measurement.

Back to Maria's Dimes and Pennies

• 1 dime = dollar. 1 penny = dollar.
• Maria's 3 dimes = — the same as Jamal's 30 pennies!
• Plus 4 more pennies: .
• That's 34 cents.

Is This Really 34 Dollars?

• We found of a dollar.
• A classmate writes the answer as "34 dollars."
• Does 3 dimes and 4 pennies really make 34 whole dollars?

Jake's Coins: Write the Equation

• Jake has 7 dimes and 25 pennies.
• Write the fraction equation and solve.
• What fraction of a dollar, and how many cents?

Measuring a Ribbon in Meters

• 1 decimeter = meter. 1 centimeter = meter.
• A ribbon piece is meter; another is meter.
• Convert and add: meter.
• That's 48 centimeters.

Working Backward to Find Tina's Dimes

• Tina has of a dollar.
• She has 6 pennies and some dimes.
• How many dimes does she have?

Four Mistakes to Watch For

— add numerators only; denominator stays 100.

— multiply both top and bottom by 10.

The shortcut only works because 10 × 10 = 100.

Keep the unit: of a dollar is 34 cents, not dollars.

What You Can Do Now

• Tenths and hundredths are the same amount, in different-sized pieces.
• Once the pieces match, adding is just counting.
• Next lesson: write these amounts as decimals, like $0.34.