🔁 Show me another way
2/5 × 3/4, solved three ways. Same answer every time. Pick the way that clicks for you.
🍎 For teachers and families: all three ways reach the same standard
New York State standard NY-5.NF.4:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction.
Part NY-5.NF.4b:
Find the area of a rectangle with fractional side lengths by tiling it with rectangles of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Source: New York State Education Department, Next Generation Mathematics Learning Standards, Grade 5 Crosswalk.
The area model (shade twice) and the number line ("2/5 of 3/4") show why the rule "top times top, bottom times bottom" works: the bottoms count all the small parts and the tops count the parts shaded twice. The answer is accepted in any equal form (6/20 or 3/10). This page covers a fraction times a fraction; a whole number times a fraction is in the lesson itself.
These ways are general mathematics. Goal100 wrote and drew them; nothing is copied from any publisher's program. Goal100 does not say which program your school uses: the learner picks by picture. Progress stays on this device.