In Grade 3 you solved multiplication and division stories about equal groups. Multiplication can also compare two amounts: "Ben has 3 times as many stickers as Ana."
Idea clave
"$k$ times as many as $m$" means $k$ groups the size of $m$, so it is $k \times m$. The equation $15 = 3 \times 5$ can be read "15 is 3 times as many as 5" (and also "15 is 5 times as many as 3").
Por qué funciona
Draw Ana's 5 stickers as one bar. "3 times as many" means Ben's bar is made of 3 bars that size. Three bars of 5 is $3 \times 5 = 15$. The bigger amount is copies of the smaller one, so you multiply.
Ejemplo resuelto: Find the bigger amount
Ana has 5 stickers. Ben has 3 times as many. How many does Ben have?
- Ben has 3 groups the size of Ana's 5.
- $3 \times 5 = 15$.
Respuesta: Ben has 15 stickers.
Ejemplo resuelto: Read an equation as a comparison
Write a comparison sentence for $24 = 4 \times 6$.
- The product, 24, is the bigger amount.
- It is 4 groups of 6.
Respuesta: 24 is 4 times as many as 6. (Also: 24 is 6 times as many as 4.)
Error común
Treating "3 times as many" as "3 more than": $5 + 3 = 8$. That answers a different question. "Times as many" makes copies, so multiply. Check: is your answer made of 3 equal parts, each the size of the smaller amount?